C. Riverside Curio

Codeforces

IDCF956C

Time1000ms

Memory256MB

Difficulty—

data structuresdpgreedyimplementation

Arkady decides to observe a river for _n_ consecutive days. The river's water level on each day is equal to some real value. Arkady goes to the riverside each day and makes a mark on the side of the channel at the height of the water level, but if it coincides with a mark made before, no new mark is created. The water does not wash the marks away. Arkady writes down the number of marks strictly above the water level each day, on the _i_\-th day this value is equal to _m__i_. Define _d__i_ as the number of marks strictly under the water level on the _i_\-th day. You are to find out the minimum possible sum of _d__i_ over all days. There are no marks on the channel before the first day. ## Input The first line contains a single positive integer _n_ (1 ≤ _n_ ≤ 105) — the number of days. The second line contains _n_ space-separated integers _m_1, _m_2, ..., _m__n_ (0 ≤ _m__i_ < _i_) — the number of marks strictly above the water on each day. ## Output Output one single integer — the minimum possible sum of the number of marks strictly below the water level among all days. [samples] ## Note In the first example, the following figure shows an optimal case. <center>![image](https://espresso.codeforces.com/6a5f9b7611c00cb9393f7740cab8d9b48172f3b1.png)</center>Note that on day 3, a new mark should be created because if not, there cannot be 3 marks above water on day 4. The total number of marks underwater is 0 + 0 + 2 + 0 + 3 + 1 = 6. In the second example, the following figure shows an optimal case. <center>![image](https://espresso.codeforces.com/2375f8b5c2e31e13f4addbe0a7c470c6493fac4d.png)</center>

Samples

Input #1

6
0 1 0 3 0 2

Output #1

Input #2

5
0 1 2 1 2

Output #2

Input #3

5
0 1 1 2 2

Output #3

API Response (JSON)

{
  "problem": {
    "name": "C. Riverside Curio",
    "description": {
      "content": "Arkady decides to observe a river for _n_ consecutive days. The river's water level on each day is equal to some real value. Arkady goes to the riverside each day and makes a mark on the side of the ",
      "description_type": "Markdown"
    },
    "platform": "Codeforces",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "CF956C"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Arkady decides to observe a river for _n_ consecutive days. The river's water level on each day is equal to some real value.\n\nArkady goes to the riverside each day and makes a mark on the side of the ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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